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lfunc_lfunctions • Show schema
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{'Lhash': '1319729532234255952849050160046', 'a10': [-1.2360679774997898, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.2360679774997898, 0.0], 'a6': [1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.82362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3234.1', 'coefficient_field': 'CDF', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [-5.23606797749979, 0], [17.0, 0]], [[1.0, 0], [-7.708203932499369, 0], [19.0, 0]], [[1.0, 0], [2.4721359549995796, 0], [23.0, 0]], [[1.0, 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'2-3234-1.1-c1-0-25', 'leading_term': '3.54955461843286310809893423909', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3234/2/a/be/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.5495546184328632, 3.5422976944748052, 3.5204123131012337, 3.4835631592863194, 3.431219204304391, 3.362693595839266, 3.2771960175644135, 3.173894501957099, 3.0519833818663176, 2.910754036467763, 2.7496652696464996, 2.568410481082192, 2.3669791813706467, 2.1457108054416283, 1.9053391562268949, 1.6470261456775268, 1.372383791422066, 1.0834836836611788, 0.7828533725091144, 0.4734593559724375, 0.15867658610345672, -0.1577553351153295, -0.4717888229578754, -0.7791370951493806, -1.075354013270301, -1.3559235896757535, -1.6163574375849281, -1.8522981189998586, -2.0596260435366416, 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'7.77917153838629961445706251782448', '8.406468254377956189503924274561270'], 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04108303344521762954040797548', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30622061104618036960300448251', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33255447285717329522932116873', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.82362001368209, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3234/2/a/be/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-3234-1.1-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04108303344521762954040797548', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1319729532234255952849050160046', 'Lhash_array': ['1319729532234255952849050160046'], 'label': '2-3234-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/be/1/1'}